Solve 3/4+2/3x=5/2x-1/6

$$\frac{ 3 }{ 4 } + \frac{ 2 }{ 3 } x= \frac{ 5 }{ 2 } x- \frac{ 1 }{ 6 }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Subtract \frac{5}{2}x from both sides.

$$\frac{3}{4}+\frac{2}{3}x-\frac{5}{2}x=-\frac{1}{6}$$

Combine \frac{2}{3}x and -\frac{5}{2}x to get -\frac{11}{6}x.

$$\frac{3}{4}-\frac{11}{6}x=-\frac{1}{6}$$

Subtract \frac{3}{4} from both sides.

$$-\frac{11}{6}x=-\frac{1}{6}-\frac{3}{4}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{1}{6} and \frac{3}{4} to fractions with denominator 12.

$$-\frac{11}{6}x=-\frac{2}{12}-\frac{9}{12}$$

Since -\frac{2}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{11}{6}x=\frac{-2-9}{12}$$

Subtract 9 from -2 to get -11.

$$-\frac{11}{6}x=-\frac{11}{12}$$

Multiply both sides by -\frac{6}{11}, the reciprocal of -\frac{11}{6}.

$$x=-\frac{11}{12}\left(-\frac{6}{11}\right)$$

Multiply -\frac{11}{12} times -\frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-11\left(-6\right)}{12\times 11}$$

Do the multiplications in the fraction \frac{-11\left(-6\right)}{12\times 11}.

$$x=\frac{66}{132}$$

Reduce the fraction \frac{66}{132} to lowest terms by extracting and canceling out 66.

$$x=\frac{1}{2}$$